含关节间隙的3-CP_aRR并联机构的运动学和动力学分析
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摘要
为研究关节间隙对并联机构动态特性的影响,以3-CP_aRR并联机构为研究对象。基于该并联机构的运动学约束,研究了该并联机构的运动学规律,表明该并联机构驱动圆柱副可等效分解为驱动移动副和被动转动副;利用正态分布概率统计模型建立了含间隙转动关节径向和轴向的运动学模型,进而建立了含关节间隙的支链运动学模型;根据关节元素间接触运动学模型,基于Flores接触力模型和修正的Coulomb摩擦模型分别建立了转动关节的法向接触力和切向接触力模型,并基于非完整系统的Lagrange方程法建立了含关节间隙并联机构的动力学模型;通过实例计算详细分析了转动关节间隙对并联机构运动学特性和动态响应的影响;此外,通过与标准正态分布模型参数μ对比,分析了定义关节元素初始接触时的间隙量为μ值时的物理意义。该研究可为其他含关节间隙多体系统的研究提供新的研究方法和理论基础。
In order to study the effect of joint clearance on the dynamic characteristics of parallel mechanisms,a3-CP_aRR parallel mechanism was taken as an example. First,the kinematics of the parallel mechanism was studied synthetically by analyzing the constraints. It shows that the cylindrical pair of the parallel mechanism can be equivalent to a driving-sliding pair and a passive-revolute pair. Next,a normal distribution statistic model was used to establish the kinematic model of the revolute joint with clearance in radial direction and axial direction,and a branch kinematics model was also established. The normal contact force between the joint elements was evaluated based on the Flores contact model,and the tangential contact force was evaluated according to the modified Coulomb friction model. Then,the dynamic model of the parallel mechanism with joint clearance was established based on the non-holonomic systems Lagrange equation method. Finally,the effect of revolute joint clearance on the parallel mechanism's kinematics and dynamic response was analyzed in detail through a numerical example. In addition,compared with the parameter of standard normal distribution model,the physical meaning of defining the initial contact clearance value as μ was analyzed.The research provides a new research approach and builds a theoretic foundation for the analysis of multi-body systems with clearance.
In order to study the effect of joint clearance on the dynamic characteristics of parallel mechanisms,a3-CP_aRR parallel mechanism was taken as an example. First,the kinematics of the parallel mechanism was studied synthetically by analyzing the constraints. It shows that the cylindrical pair of the parallel mechanism can be equivalent to a driving-sliding pair and a passive-revolute pair. Next,a normal distribution statistic model was used to establish the kinematic model of the revolute joint with clearance in radial direction and axial direction,and a branch kinematics model was also established. The normal contact force between the joint elements was evaluated based on the Flores contact model,and the tangential contact force was evaluated according to the modified Coulomb friction model. Then,the dynamic model of the parallel mechanism with joint clearance was established based on the non-holonomic systems Lagrange equation method. Finally,the effect of revolute joint clearance on the parallel mechanism's kinematics and dynamic response was analyzed in detail through a numerical example. In addition,compared with the parameter of standard normal distribution model,the physical meaning of defining the initial contact clearance value as μ was analyzed.The research provides a new research approach and builds a theoretic foundation for the analysis of multi-body systems with clearance.
引文
[1]REIS V L,DANIEL G B,CAVALCA K L.Dynamic analysis of a lubricated planar slider-crank mechanism considering friction and Hertz contact effects[J].Mechanism and Machine Theory,2014,74(6):257-273.
[2]CHRISTOPHE B,LAURENT Z.An approach for predicting the internal behaviour of ball bearings under high moment load[J].Mechanism and Machine Theory,2016,101:1-22.
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[6]ZHAO Haiyang,XU Minqiang,WANG Jindong,et al.Aparameters optimization method for planar joint clearance model and its application for dynamics simulation of reciprocating compressor[J].Journal of Sound and Vibration,2015,344:416-433.
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[9]ERKAYA S.Prediction of vibration characteristics of a planar mechanism having imperfect joints using neural network[J].Journal of Mechanical Science and Technology,2012,26(5):1419-1430.
[10]BAI Zhengfeng,ZHAO Yang.A hybrid contact force model of revolute joint with clearance for planar mechanical systems[J].International Journal of Non-Linear Mechanics,2013,48:15-36.
[11]FLORES P,KOSHY C,LANKARANI H,et al.Numerical and experimental investigation on multibody systems with revolute clearance joints[J].Nonlinear Dynamics,2011,65(4):383-398.
[12]FLORES P.A parametric study on the dynamic response of planar multibody systems with multiple[J].Nonlinear Dynamics,2010,61(4):633-653.
[13]XU Lixin,YANG Yuhu,LI Yonggang,et al.Modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance[J].Mechanism and Machine Theory,2012,56:69-88.
[14]XU Lixin,LI Yonggang.Investigation of joint clearance effects on the dynamic performance of a planar 2-DOF pickand-place parallel manipulator[J].Robotics and ComputerIntegrated Manufacturing,2014,30(1):62-73.
[15]XU Lixin,YANG Yuhu.Modeling a non-ideal rolling ball bearing joint with localized defects in planar multibody systems[J].Multibody System Dynamics,2015,35(4):409-426.
[16]PEREIRA C,AMBRSIO J,RAMALHO A.Dynamics of chain drives using a generalized revolute clearance joint formulation[J].Mechanism and Machine Theory,2015,92:64-85.
[17]MUVENGEI O,KIHIU J,IKUA B.Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints[J].Nonlinear Dynamics,2013,73(1/2):259-273.
[18]MUVENGEI O,KIHIU J,IKUA B.Numerical study of parametric effects on the dynamic response of planar multibody systems with differently located frictionless revolute clearance joints[J].Mechanism and Machine Theory,2012,53(7):30-49.
[19]VAREDI S,DANIALI H,DARDEL M,et al.Optimal dynamic design of a planar slider-crank mechanism with a joint clearance[J].Mechanism and Machine Theory,2015,86:191-200.
[20]BAI Zhengfeng,ZHAO Yang.Dynamics modeling and quantitative analysis of multibody systems including revolute clearance joint[J].Precision Engineering,2012,36(4):554-567.
[21]ZHAO Bo,ZHANG Zhinan,FANG Congcong,et al.Modeling and analysis of planar multibody system with mixed lubricated revolute joint[J].Tribology International,2016,98:229-241.
[22]ZHAO Bo,ZHOU Kun,XIE Youbai.A new numerical method for planar multibody system with mixed lubricated revolute joint[J].International Journal of Mechanical Sciences,2016,113:105-119.
[23]ERKAYA S,DOGˇAN S,ULUS S.Effects of joint clearance on the dynamics of a partly compliant mechanism:numerical and experimental studies[J].Mechanism and Machine Theory,2015,88:125-140.
[24]ERKAYA S,DOGˇAN S.A comparative analysis of joint clearance effects on articulated and partly compliant mechanisms[J].Nonlinear Dynamics,2015,81(1/2):323-341.
[25]ERKAYA S,UZMAY I.Modeling and simulation of joint clearance effects on mechanisms having rigid and flexible links[J].Journal of Mechanical Science and Technology,2014,28(8):2979-2986.
[26]王庚祥,刘宏昭.考虑球面副间隙的4-SPS/CU并联机构动力学分析[J].机械工程学报,2015,51(1):43-51.WANG Gengxiang,LIU Hongzhao.Dynamics analysis of 4-SPS/CU parallel mechanism with spherical joint clearance[J].Journal of Mechanical Engineering,2015,51(1):43-51.
[27]DUBOWSKY S,GARDNER T N.Design and analysis of muitilink flexible mechanisms with multiple clearance connection[J].Journal of Engineering for Industry,1997,99(7):88-96.
[28]侯雨雷,汪毅,井国宁,等.含间隙RU-RPR解耦并联机构混沌与冲击现象[J].振动与冲击,2017,36(1):215-222.HOU Yulei,WANG Yi,JING Guoning,et al.Chaos and impact phenomena of a RU-RPR decoupled parallel mechanism containing clearance[J].Journal of Vibration and Shock,2017,36(1):215-222.
[29]GAO X D,YAMAMOTO M,MOHRI A.Application of fuzzy logic controller in the seam tracking of arc-welding robot[C]∥Proceedings of Industrial Electronics,Control and Instrumentation.New Orleans:IEEE,1997.
[30]WU W D,RAO S S.Interval approach for the modeling of tolerances and clearances in mechanism analysis[J].Journal of Mechanical Design,2004,126(4):581-592.
[31]王庚祥,刘宏昭,邓培生.考虑球面副间隙的并联机构动力学模型[J].振动与冲击,2014,33(10):43-49.WANG Gengxiang,LIU Hongzhao,DENG Peisheng.Dynamic modeling for a parallel mechanism considering spherical joint clearance[J].Journal of Vibration and Shock,2014,33(10):43-49.
[32]YAN Shaoze,XIANG Wuweikai,ZHANG Lin.Acomprehensive model for 3D revolute joints with clearances in mechanical systems[J].Nonlinear Dynamics,2015,80(1/2):309-328.
[33]FLORES P,AMBROSIO J,CLARO J C P,et al.Influence of the contact-impact force model on the dynamic response of multi-body systems[J].Proceedings of the Institution of Mechanical Engineers,Part K:Journal of Multi-Body Dynamics,2006,220(1):21-34.
[34]AMBROSIO J.Impact of rigid and flexible multibody systems:deformation description and contact models[J].Virtual Nonlinear Multibody Systems,2003,103:57-81.
[2]CHRISTOPHE B,LAURENT Z.An approach for predicting the internal behaviour of ball bearings under high moment load[J].Mechanism and Machine Theory,2016,101:1-22.
[3]QUENTAL C,FOLGADO J,AMBRSIO J,et al.A new shoulder model with a biologically inspired glenohumeral joint[J].Medical Engineering and Physics,2016,38(9):969-977.
[4]FRISOLI A,SOLAZZI M,PELLEGRINETTI D,et al.A new screw theory method for the estimation of position accuracy in spatial parallel manipulators with revolute joint clearances[J].Mechanism and Machine Theory,2011,46(12):1929-1949.
[5]CHEN Genliang,WANG Hao,LIN Zhongqin.A unified approach to the accuracy analysis of planar parallel manipulators both with input uncertainties and joint clearance[J].Mechanism and Machine Theory,2013,64(6):1-17.
[6]ZHAO Haiyang,XU Minqiang,WANG Jindong,et al.Aparameters optimization method for planar joint clearance model and its application for dynamics simulation of reciprocating compressor[J].Journal of Sound and Vibration,2015,344:416-433.
[7]KOSHY C S,FLORESl P,LANKARANI H M.Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints:computational and experimental approaches[J].Nonlinear Dynamics,2013,73(1/2):325-338.
[8]PEREIRA C,RAMALHO A,AMBRSIO J.Applicability domain of internal cylindrical contact force models[J].Mechanism and Machine Theory,2014,78(8):141-157.
[9]ERKAYA S.Prediction of vibration characteristics of a planar mechanism having imperfect joints using neural network[J].Journal of Mechanical Science and Technology,2012,26(5):1419-1430.
[10]BAI Zhengfeng,ZHAO Yang.A hybrid contact force model of revolute joint with clearance for planar mechanical systems[J].International Journal of Non-Linear Mechanics,2013,48:15-36.
[11]FLORES P,KOSHY C,LANKARANI H,et al.Numerical and experimental investigation on multibody systems with revolute clearance joints[J].Nonlinear Dynamics,2011,65(4):383-398.
[12]FLORES P.A parametric study on the dynamic response of planar multibody systems with multiple[J].Nonlinear Dynamics,2010,61(4):633-653.
[13]XU Lixin,YANG Yuhu,LI Yonggang,et al.Modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance[J].Mechanism and Machine Theory,2012,56:69-88.
[14]XU Lixin,LI Yonggang.Investigation of joint clearance effects on the dynamic performance of a planar 2-DOF pickand-place parallel manipulator[J].Robotics and ComputerIntegrated Manufacturing,2014,30(1):62-73.
[15]XU Lixin,YANG Yuhu.Modeling a non-ideal rolling ball bearing joint with localized defects in planar multibody systems[J].Multibody System Dynamics,2015,35(4):409-426.
[16]PEREIRA C,AMBRSIO J,RAMALHO A.Dynamics of chain drives using a generalized revolute clearance joint formulation[J].Mechanism and Machine Theory,2015,92:64-85.
[17]MUVENGEI O,KIHIU J,IKUA B.Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints[J].Nonlinear Dynamics,2013,73(1/2):259-273.
[18]MUVENGEI O,KIHIU J,IKUA B.Numerical study of parametric effects on the dynamic response of planar multibody systems with differently located frictionless revolute clearance joints[J].Mechanism and Machine Theory,2012,53(7):30-49.
[19]VAREDI S,DANIALI H,DARDEL M,et al.Optimal dynamic design of a planar slider-crank mechanism with a joint clearance[J].Mechanism and Machine Theory,2015,86:191-200.
[20]BAI Zhengfeng,ZHAO Yang.Dynamics modeling and quantitative analysis of multibody systems including revolute clearance joint[J].Precision Engineering,2012,36(4):554-567.
[21]ZHAO Bo,ZHANG Zhinan,FANG Congcong,et al.Modeling and analysis of planar multibody system with mixed lubricated revolute joint[J].Tribology International,2016,98:229-241.
[22]ZHAO Bo,ZHOU Kun,XIE Youbai.A new numerical method for planar multibody system with mixed lubricated revolute joint[J].International Journal of Mechanical Sciences,2016,113:105-119.
[23]ERKAYA S,DOGˇAN S,ULUS S.Effects of joint clearance on the dynamics of a partly compliant mechanism:numerical and experimental studies[J].Mechanism and Machine Theory,2015,88:125-140.
[24]ERKAYA S,DOGˇAN S.A comparative analysis of joint clearance effects on articulated and partly compliant mechanisms[J].Nonlinear Dynamics,2015,81(1/2):323-341.
[25]ERKAYA S,UZMAY I.Modeling and simulation of joint clearance effects on mechanisms having rigid and flexible links[J].Journal of Mechanical Science and Technology,2014,28(8):2979-2986.
[26]王庚祥,刘宏昭.考虑球面副间隙的4-SPS/CU并联机构动力学分析[J].机械工程学报,2015,51(1):43-51.WANG Gengxiang,LIU Hongzhao.Dynamics analysis of 4-SPS/CU parallel mechanism with spherical joint clearance[J].Journal of Mechanical Engineering,2015,51(1):43-51.
[27]DUBOWSKY S,GARDNER T N.Design and analysis of muitilink flexible mechanisms with multiple clearance connection[J].Journal of Engineering for Industry,1997,99(7):88-96.
[28]侯雨雷,汪毅,井国宁,等.含间隙RU-RPR解耦并联机构混沌与冲击现象[J].振动与冲击,2017,36(1):215-222.HOU Yulei,WANG Yi,JING Guoning,et al.Chaos and impact phenomena of a RU-RPR decoupled parallel mechanism containing clearance[J].Journal of Vibration and Shock,2017,36(1):215-222.
[29]GAO X D,YAMAMOTO M,MOHRI A.Application of fuzzy logic controller in the seam tracking of arc-welding robot[C]∥Proceedings of Industrial Electronics,Control and Instrumentation.New Orleans:IEEE,1997.
[30]WU W D,RAO S S.Interval approach for the modeling of tolerances and clearances in mechanism analysis[J].Journal of Mechanical Design,2004,126(4):581-592.
[31]王庚祥,刘宏昭,邓培生.考虑球面副间隙的并联机构动力学模型[J].振动与冲击,2014,33(10):43-49.WANG Gengxiang,LIU Hongzhao,DENG Peisheng.Dynamic modeling for a parallel mechanism considering spherical joint clearance[J].Journal of Vibration and Shock,2014,33(10):43-49.
[32]YAN Shaoze,XIANG Wuweikai,ZHANG Lin.Acomprehensive model for 3D revolute joints with clearances in mechanical systems[J].Nonlinear Dynamics,2015,80(1/2):309-328.
[33]FLORES P,AMBROSIO J,CLARO J C P,et al.Influence of the contact-impact force model on the dynamic response of multi-body systems[J].Proceedings of the Institution of Mechanical Engineers,Part K:Journal of Multi-Body Dynamics,2006,220(1):21-34.
[34]AMBROSIO J.Impact of rigid and flexible multibody systems:deformation description and contact models[J].Virtual Nonlinear Multibody Systems,2003,103:57-81.